The exponential of a constant matrix on time scales

Zafer, Ağacık
In this paper we describe an elementary method for calculating the matrix exponential on an arbitrary time scale. An example is also given to illustrate the result.


The momentum four-vector in Brans-Dicke wormholes
Pirinccioglu, Nurettin; Acikgoez, Irfan; Salti, Mustafa (Springer Science and Business Media LLC, 2007-05-01)
In this work, in order to compute energy and momentum distributions (due to matter plus fields including gravitation) associated with the Brans-Dicke wormhole solutions we consider Moller's energy-momentum complexes both in general relativity and the teleparallel gravity, and the Einstein energy-momentum formulation in general relativity. We find exactly the same energy and momentum in three of the formulations. The results obtained in teleparallel gravity is also independent of the teleparallel dimensionle...
Analytical solution of the Schrodinger equation for Makarov potential with any l angular momentum
Bayrak, O.; Karakoc, M.; Boztosun, I.; Sever, Ramazan (Springer Science and Business Media LLC, 2008-11-01)
We present the analytical solution of the Schrodinger Equation for the Makarov potential within the framework of the asymptotic iteration method for any n and l quantum numbers. Energy eigenvalues and the corresponding wave functions are calculated. We also obtain the same results for the ring shaped Hartmann potential which is the special form of the non-central Makarov potential.
Displaceability of Certain Constant Sectional Curvature Lagrangian Submanifolds
Şirikçi, Nil İpek (Springer Science and Business Media LLC, 2020-10-01)
We present an alternative proof of a nonexistence result for displaceable constant sectional curvature Lagrangian submanifolds under certain assumptions on the Lagrangian submanifold and on the ambient symplectically aspherical symplectic manifold. The proof utilizes an index relation relating the Maslov index, the Morse index and the Conley-Zehnder index for a periodic orbit of the flow of a specific Hamiltonian function, a result on this orbit's Conley-Zehnder index and another result on the Morse indices...
A model for the computation of quantum billiards with arbitrary shapes
Erhan, Inci M.; Taşeli, Hasan (Elsevier BV, 2006-10-01)
An expansion method for the stationary Schrodinger equation of a three-dimensional quantum billiard system whose boundary is defined by an arbitrary analytic function is introduced. The method is based on a coordinate transformation and an expansion in spherical harmonics. The effectiveness is verified and confirmed by a numerical example, which is a billiard system depending on a parameter.
A General Approach for the Exact Solution of the Schrodinger Equation
TEZCAN, CEVDET; Sever, Ramazan (Springer Science and Business Media LLC, 2009-02-01)
The Schrodinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schrodinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.
Citation Formats
A. Zafer, “The exponential of a constant matrix on time scales,” ANZIAM JOURNAL, pp. 99–106, 2006, Accessed: 00, 2020. [Online]. Available: